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Proof step 267 from proof inv-write (previous step)

m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files[ino] = mkfile(m3, md1, m4, content1), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md0, # links(m, dirs), content0), files[m] = mkfile(m2, md, # links(m, dirs), content), dirs[ino] = mkdir(m7, md3, m8, m9, entries), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, mkfile(m3, md1, m4, content1) = mkfile(m5, md2, m6, content2), dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, ROOT_INO ∈ dirs, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ ino = m, ino4 = 0, n = 0, n2 = 0, of-cons(of[fd, mkfile(m, mode, m0 + ino4)], dirs, files[m, mkfile(m0 + ino4, md0, # links(m, dirs), content)]) ∧ ( (ino ∈ dirs ∧ ino ≠ ROOT_INO ∧ links(ino, dirs) = ∅ → entries = ∅) ∧ (ino ∈ dirs → m8 = # links(ino, dirs) ∧ # links(ino, dirs) ≤ 1 ∧ m7 = # entries ∧ m9 = # subdirs(ino, dirs)) ∧ (ino ∈ files → ¬ ino ∈ dirs ∧ m4 = # links(ino, dirs)) ∧ (ino ∈ dirs ∧ name ∈ entries → entries[name] ∈ dirs ∨ entries[name] ∈ files) → (ino ∈ files → ¬ ino ∈ dirs ∧ m6 = # links(ino, dirs)) ∧ (ino ∈ files ∧ n0 ∈ content2 → # content2[n0] = VFS_PAGE_SIZE)), err1 = ESUCCESS ∧ ¬ isdir, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 268:
⊦ of-cons(of0, dirs0, files0) → (of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1))
Proof step 269:
m1 + n1 = m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE + VFS_PAGE_SIZE, files[ino] = mkfile(m3, md1, m6, content2), of[fd] = mkfile(m, mode, m0), files1[m] = mkfile(m1, md0, # links(m, dirs), content0), files[m] = mkfile(m2, md, # links(m, dirs), content), dirs[ino] = mkdir(m7, md3, m8, m9, entries), m1 = n2 + m1 / VFS_PAGE_SIZE * VFS_PAGE_SIZE, dom of < ino3, m1 < m0 + ino4, afs-cons(dirs, files), afs-cons(dirs, files1), of-cons(of, dirs, files), of-cons(of, dirs, files1), m ∈ files1, m1 / VFS_PAGE_SIZE ∈ content0, fd ∈ of, m ∈ files, ROOT_INO ∈ dirs, n0 ∈ of[fd, mkfile(m, mode, m0 + ino4)], n0 ∈ of, of[n0].ino ∈ files1, m1 % VFS_PAGE_SIZE + n1 ≤ VFS_PAGE_SIZE, n ≤ # buf0, n2 + n1 ≤ VFS_PAGE_SIZE ⊦ ino = m, ino4 = 0, n = 0, n2 = 0, of[fd, mkfile(m, mode, m0 + ino4)][n0].ino ∈ files, err1 = ESUCCESS ∧ ¬ isdir, mode ≠ MODE_W ∧ mode ≠ MODE_RW

Rule argument

Additional information

Used simplifier rules: of-cons-reduce: ⊦ of-cons(of0, dirs0, files0) → ( of-cons(of1, dirs1, files1) ↔ (∀ n. (n ∈ of0 → of0[n].ino ∈ files0) → n ∈ of1 → of1[n].ino ∈ files1));%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)% ⊦ mkfile(m, mode, m0).ino = m; (s)% ⊦ fd = fd0 → of[fd0, file][fd] = file; (s)% ⊦ fd ∈ of[fd0, file] ↔ fd = fd0 ∨ fd ∈ of; (ws)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)